# CLASS-8PROBLEM & SOLUTION OF CIRCLE

Example.1) Find the circumference and diameter of the circle where radius is 28 cm

Ans.)  As per the given condition, the radius (r) of the given circle is = 28 cm

As per the formula, circumference of a circle (C) = 2 πr

22

=  2 X ------- X 28  = 2 X 22 X 4 = 176 cm ………….(1)

7

Now, area of the said circle is = π r²

22

= ------- X (28)² = 22 X 4 X 28  = 2464 cm²………………..(2)    (Ans.)

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Example.2) If the area of the circle is 7546 cm², then find the radius and circumference of the same circle

Ans.) as per the given condition, the area of the given circle is 7546 cm²

as we know the formula of the area of the circle is = πr²

so, as per the given condition, πr² = 7546 cm²

22

or, -------- r² =  7546

7

7546 X 7

Or,   r²  =  ------------ 343 X 7 = 2401

22

Or,    r = √49² =  49 cm ………………. (1)

Now, as we know the formula of the circumference (C) = 2 π r

22

=  2 X ------- X 49 = 2 X 22 X 7 = 308 cm ………......…(2)     (Ans.)

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Example.3) If, the wheel of a school bus has a diameter of 84 cm, calculate

a) the distance traveled by the school bus after on rotation of the wheel and

b) the number of the rotation of the wheel if the school bus covers a distance of 1.65km

84

Ans.) Here the radius (r) of the wheel = -------- = 42

2

Diameter (D)

[ as we know that Radius (r) = ---------------- ]

2

a) the distance traveled by the school bus after one rotation of the wheel

as we know that, the circumference of the wheel is = 2 π r

=  2 X 22/7 X 42 cm = 264 cm

b) the school bus covers 264 cm in 1 rotation of the wheel

1

so, the school bus cover 1 cm in ------- of a rotation of the wheel

264

The school bus will cover 1.65 km,

1.65 X 1000 X 100

which is 1.65 X 1000 X 100 cm in --------------- rotation of the wheel

264

[ As we know 1 km = 1000 m and 1 m = 100 cm625 rotation

So, the number of the rotation is 625 rotation          (Ans.)